The petition, filed this week, challenges a second execution by any means, arguing it's "a violation of double jeopardy and the prohibition on cruel and unusual punishment".

Hamm has been on death row for decades after killing a motel worker.

Mr Harcourt argued authorities had been warned any attempt to administer the drug would result in "unnecessary pain and suffering" which was in violation of US law.

He also said an alternative method of execution via an oral lethal injection would not have needed to use his veins and therefore would have avoided a "botched, bloody, and cruel attempt at intravenous lethal injection".

"What resulted was a prolonged, exceedingly painful, bloody, and botched attempt to execute Doyle Hamm through his lower extremities and right groin. None of this was unforeseeable," the petition argues.

"Physically, as he was strapped down to the lethal injection gurney in the execution chamber knowing that he was about to die, Doyle Hamm was jabbed multiple times with needles and catheters in his ankles, shin, and right groin," the petition continues.

"Psychologically, once again strapped to his death gurney, Doyle Hamm was so injured that he hoped the execution team would succeed so that it would be over with and he would be dead."

Hamm was stabbed a total of five times, three in one leg and two on the other.

An ultrasound team attempted to find a vein in his groin, resulting in another six jabs, and left him bleeding.